Higher Distance Commuting Varieties by Prof. Ralph Morrison, Williams College, at the Mathematics Faculty Seminar, November 2, 1 – 1:45 pm, Stetson Court Classroom 105

Higher Distance Commuting Varieties by Prof. Ralph Morrison, Williams College, at the Mathematics Faculty Seminar, November 2, 1 – 1:45 pm, Stetson Court Classroom 105

Abstract:  The set of all pairs of matrices that commute under multiplication can be described using polynomial equations. This means that this set is an affine variety, and can be studied using the powerful tools of algebraic geometry. To generalize this, we define a commuting distance between any two matrices, which measures how far they are from commuting with one another. We consider the set of pairs of matrices at most a fixed commuting distance apart, and prove that this set is also an affine variety, at least when working over an algebraically closed field. We also discuss what can go wrong over other fields. (This is joint work with Madeleine Elyse ’18 and Alexander Guterman.)